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Originally Posted by Kent
I read a popular science book, and in one chapter it talks about transfinite numbers.
i have some questions.
Can the power set of the continum be enumerated? I have no idea how you imagine a power set of a power set of a continum? Are their pictures?
what are the application for the power set of a set?
what are your thoughts on transfinit numbers?
any problems?
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I can help a little bit. You acknowledge that there are an infinite number of integers. In fact you can
enumerate them. The same for the rationals. There is a proof that I am unable to give there are as many
rationals as integers. However, the quantity of reals are more than the integers. Cantor came up with a
notion of transfinite numbers or "levels of infinity". The number of integers are assigned Aleph 0 (naught),
for the subscripted Hebrew character. Number of reals is Aleph 1. The number of continuous functions over
the reals Rn is Aleph 2. And so on. For more info, do a google search on Cantor and Transfinite numbers.
Maddog
